Quantile-Based Test for Heterogeneous Treatment Effects

We introduce a permutation test for heterogeneous treatment effects based on the quantile process. However, tests based on the quantile process often suffer from estimated nuisance parameters that jeopardize their validity, even in large samples. To overcome this problem, we use Khmaladze's martingale transformation. We show that the permutation test based on the transformed statistic controls size asymptotically. Numerical evidence asserts the good size and power performance of our test procedure compared to other popular quantile-based tests. We discuss a fast implementation algorithm and illustrate our method using experimental data from a welfare reform.